The wide and increasing availability of collected data in the form of trajectories has led to research advances in behavioral aspects of the monitored subjects (e.g., wild animals, people, and vehicles). Using trajectory data harvested by devices, such as GPS, RFID and mobile devices, complex pattern queries can be posed to select trajectories based on specific events of interest. In this paper, we present a study on FPGA- and GPU-based architectures processing complex patterns on streams of spatio-temporal data. Complex patterns are described as regular expressions over a spatial alphabet that can be implicitly or explicitly anchored to the time domain. More importantly, variables can be used to substantially enhance the flexibility and expressive power of pattern queries. Here we explore the challenges in handling several constructs of the assumed pattern query language, with a study on the trade-offs between expressiveness, scalability and matching accuracy. We show an extensive performance evaluation where FPGA and GPU setups outperform the current state-of-the-art (single-threaded) CPU-based approaches, by over three orders of magnitude for FPGAs (for expressive queries) and up to two orders of magnitude for certain datasets on GPUs (and in some cases slowdown). Unlike software-based approaches, the performance of the proposed FPGA and GPU solutions is only minimally affected by the increased pattern complexity.